The consensus appears to be that after the Gokumyo 20k paste should not be necessary.

I too have left the paste out for the first few months, but some of my razors respond well to CrOx paste after refreshing the edge with the Naniwa 12k and Gokumyo 20k.
It seems to eliminate the harshness of the first 2-3 shaves and makes for a smoother initial edge and shave.

Leaving alone the discussion of similar grit size for both Gokumyo 20k and green CrOx paste, I could imagine that this has to do with the opposing direction that the edge is polished on the hone and on the strop.

One thing I have noticed is that using a paste after the 20k makes for a longer lasting edge, but one that isn't quite so sharp. No surprises there, I suppose! You might avoid the initial shaves being a bit less than perfect with an extended strop on the canvas, and not need the paste at all. In the end, whatever works for you and gets the beard cut is what's right!

My theory is that honing removes material from the edge only in one direction, while stropping with paste removes material only in the opposite direction, thereby smoothing an edge that has only seen one-directional abrasion on the hones.

Have ordered an inexpensive USB microscope to see whether I can find any evidence for this theory.
Will report back if the USB microscops shold provide any insights.

Got the 200X USB microscope, but at this magnification I could not detect a discernible difference in the appearance of the edge before and after stropping with paste...

I had bought the razor in question together with an otherwise identical razor, the only difference being the point (this one round the other one Spanish).

To have a reasonable comparision I took the round point through the Nanaiwa 12k, Gokomyo 20k and CrOx and the Spanish point only through the Naniwa 12k and Gokumyo 20k.

Still felt that that round point was not quite there.
Even if they were bought together and made by the same man (Aust), I still felt a difference, but it may have nothing to do with stropping with paste after the Gokumyo.

So I guess, I can leave the paste on the shelf after all...

Or to quote my old chemistry teacher when an experiment failed to produce the desired results: "And as we all can see.... ...we see nothing!"